The course teaches latest achievements in the physical modeling and numerical simulation using the Finite Element (FE) method for coupled field problems, as arising in mechatronic systems (e.g., electromagnetic brake systems, eddy current brakes, flow induced sound of air-conditioning systems, induction heating systems, etc.). Graduate students will have the following knowledge:

• physical and mathematical modeling of flow induced sound (aeroacoustics), electromagnetic-mechanical and electromagnetic-thermal systems
• FE simulations of coupled field problems towards aeroacoustics, electromagnetic-mechanical and electromagnetic-thermal systems
• correct physical interpretation of FE simulation results to perform the necessary steps to optimize current and future mechatronic systems.

The accurate modeling of mechatronic systems leads to so-called multi-field problems, which are described by a system of non-linear partial differential equations. These systems cannot be solved analytically and thus numerical calculation schemes have to be applied. Thereby, the finite element (FE) method has been established as the standard method for numerically solving the coupled system of partial differential equations describing the physical fields including their couplings.

Students will discuss and simulate various physical applications. In detail, the course will teach the physical / mathematical modelling and its FE simulation of the following coupled fields

Aeroacoustics

• Sound generation by turbulent flows according to Lighthill's analogy
• Approximation of free field conditions by absorbing boundary conditions and the Perfectly Matched Layer (PML) technique
• Non-conforming finite elements

Electromagnetics-mechanics

• Vector potential formulation for magnetodynamics
• Nonlinear finite elements (Newton method) using edge finite elements
• Coupling mechanism (electromagnetic forces, motional electromotive force)
• FE formulation for the coupled field problem including moving / deforming solid bodies

Elektromagnetics-Heat

• Multi-harmonic ansatz for the solution of the nonlinear electromagnetic partial differential equations in the frequency domain
• Finite elements of higher order to efficiently resolve eddy currents in electric conductive structures
• Coupling mechanism (Joul's losses due to currents, temperature dependet material parameters)